## [1] "explicated variable of regression : rh98"
## [1] "for  Guinean_forest-savanna_regression_rh98.RDS"           
## [2] "for  Northern_Congolian_Forest-Savanna_regression_rh98.RDS"
## [3] "for  Sahelian_Acacia_savanna_regression_rh98.RDS"          
## [4] "for  Southern_Congolian_forest-savanna_regression_rh98.RDS"
## [5] "for  West_Sudanian_savanna_regression_rh98.RDS"            
## [6] "for  Western_Congolian_forest-savanna_regression_rh98.RDS" 
## [1] "########################################"
## [1] "########################################"
## [1] "########################################"
## [1] "below, stancode for Guinean_forest-savanna_regression_rh98.RDS"
## // generated with brms 2.20.4
## functions {
## }
## data {
##   int<lower=1> N;  // total number of observations
##   vector[N] Y;  // response variable
##   int<lower=1> K;  // number of population-level effects
##   matrix[N, K] X;  // population-level design matrix
##   int<lower=1> Kc;  // number of population-level effects after centering
##   int prior_only;  // should the likelihood be ignored?
## }
## transformed data {
##   matrix[N, Kc] Xc;  // centered version of X without an intercept
##   vector[Kc] means_X;  // column means of X before centering
##   for (i in 2:K) {
##     means_X[i - 1] = mean(X[, i]);
##     Xc[, i - 1] = X[, i] - means_X[i - 1];
##   }
## }
## parameters {
##   vector[Kc] b;  // regression coefficients
##   real Intercept;  // temporary intercept for centered predictors
##   real<lower=0> shape;  // shape parameter
## }
## transformed parameters {
##   real lprior = 0;  // prior contributions to the log posterior
##   lprior += student_t_lpdf(Intercept | 3, 2, 2.5);
##   lprior += gamma_lpdf(shape | 0.01, 0.01);
## }
## model {
##   // likelihood including constants
##   if (!prior_only) {
##     // initialize linear predictor term
##     vector[N] mu = rep_vector(0.0, N);
##     mu += Intercept + Xc * b;
##     mu = exp(mu);
##     target += gamma_lpdf(Y | shape, shape ./ mu);
##   }
##   // priors including constants
##   target += lprior;
## }
## generated quantities {
##   // actual population-level intercept
##   real b_Intercept = Intercept - dot_product(means_X, b);
## }
## [1] "########################################"
## [1] "########################################"
## [1] "########################################"
## [1] " "
## [1] " "
## [1] "Guinean_forest-savanna_regression_rh98.RDS"
## [1] "########################################"
##  Family: gamma 
##   Links: mu = log; shape = identity 
## Formula: rh98 ~ fire_freq_std + mean_precip_std 
##    Data: table_region (Number of observations: 1725) 
##   Draws: 4 chains, each with iter = 10000; warmup = 2000; thin = 10;
##          total post-warmup draws = 3200
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           1.96      0.03     1.91     2.02 1.00     3075     3028
## fire_freq_std       0.03      0.01     0.01     0.05 1.00     3072     3045
## mean_precip_std     0.06      0.01     0.04     0.09 1.00     3046     3023
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape     3.80      0.12     3.56     4.04 1.00     3076     3171
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## [1] "########################################"
## [1] "Northern_Congolian_Forest-Savanna_regression_rh98.RDS"
## [1] "########################################"
##  Family: gamma 
##   Links: mu = log; shape = identity 
## Formula: rh98 ~ fire_freq_std + mean_precip_std 
##    Data: table_region (Number of observations: 243) 
##   Draws: 4 chains, each with iter = 10000; warmup = 2000; thin = 10;
##          total post-warmup draws = 3200
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           2.13      0.19     1.76     2.49 1.00     3075     3089
## fire_freq_std      -0.03      0.03    -0.09     0.04 1.00     3042     3003
## mean_precip_std    -0.00      0.09    -0.17     0.17 1.00     3065     3131
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape     5.01      0.45     4.15     5.91 1.00     3021     3166
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## [1] "########################################"
## [1] "Sahelian_Acacia_savanna_regression_rh98.RDS"
## [1] "########################################"
##  Family: gamma 
##   Links: mu = log; shape = identity 
## Formula: rh98 ~ fire_freq_std + mean_precip_std 
##    Data: table_region (Number of observations: 5563) 
##   Draws: 4 chains, each with iter = 10000; warmup = 2000; thin = 10;
##          total post-warmup draws = 3200
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           1.32      0.01     1.31     1.33 1.00     3297     3124
## fire_freq_std       0.11      0.01     0.10     0.12 1.00     3220     3216
## mean_precip_std     0.33      0.01     0.31     0.35 1.00     3299     3134
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape    18.01      0.34    17.34    18.69 1.00     3452     3136
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## [1] "########################################"
## [1] "Southern_Congolian_forest-savanna_regression_rh98.RDS"
## [1] "########################################"
##  Family: gamma 
##   Links: mu = log; shape = identity 
## Formula: rh98 ~ fire_freq_std + mean_precip_std 
##    Data: table_region (Number of observations: 47) 
##   Draws: 4 chains, each with iter = 10000; warmup = 2000; thin = 10;
##          total post-warmup draws = 3200
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           3.37      0.65     2.10     4.68 1.00     3137     3092
## fire_freq_std      -0.08      0.04    -0.16     0.01 1.00     2968     3183
## mean_precip_std    -0.96      0.31    -1.57    -0.36 1.00     3195     3092
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape     6.07      1.25     3.88     8.75 1.00     3131     2904
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## [1] "########################################"
## [1] "West_Sudanian_savanna_regression_rh98.RDS"
## [1] "########################################"
##  Family: gamma 
##   Links: mu = log; shape = identity 
## Formula: rh98 ~ fire_freq_std + mean_precip_std 
##    Data: table_region (Number of observations: 3277) 
##   Draws: 4 chains, each with iter = 10000; warmup = 2000; thin = 10;
##          total post-warmup draws = 3200
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           1.22      0.02     1.19     1.25 1.00     3067     3114
## fire_freq_std       0.08      0.01     0.07     0.10 1.00     3044     3056
## mean_precip_std     0.53      0.02     0.50     0.56 1.00     3052     2874
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape     5.47      0.13     5.21     5.73 1.00     3600     2875
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## [1] "########################################"
## [1] "Western_Congolian_forest-savanna_regression_rh98.RDS"
## [1] "########################################"
##  Family: gamma 
##   Links: mu = log; shape = identity 
## Formula: rh98 ~ fire_freq_std + mean_precip_std 
##    Data: table_region (Number of observations: 259) 
##   Draws: 4 chains, each with iter = 10000; warmup = 2000; thin = 10;
##          total post-warmup draws = 3200
## 
## Population-Level Effects: 
##                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept           1.36      0.16     1.05     1.66 1.00     2982     3193
## fire_freq_std      -0.05      0.02    -0.10    -0.00 1.00     2648     2861
## mean_precip_std     0.36      0.10     0.18     0.56 1.00     3026     3172
## 
## Family Specific Parameters: 
##       Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## shape     3.07      0.26     2.61     3.60 1.00     3508     3132
## 
## Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).

## [1] "########################################"
## [1] "Gamma regressions for  Guinean_forest-savanna_regression_rh98.RDS"           
## [2] "Gamma regressions for  Northern_Congolian_Forest-Savanna_regression_rh98.RDS"
## [3] "Gamma regressions for  Sahelian_Acacia_savanna_regression_rh98.RDS"          
## [4] "Gamma regressions for  Southern_Congolian_forest-savanna_regression_rh98.RDS"
## [5] "Gamma regressions for  West_Sudanian_savanna_regression_rh98.RDS"            
## [6] "Gamma regressions for  Western_Congolian_forest-savanna_regression_rh98.RDS"
## [1] "########################################"
## [1] "########################################"
## [1] "########################################"
## [1] "Guinean_forest-savanna_regression_rh98.RDS"
## [1] "########################################"
## [1] "dim(linear_predictors_for_one_beta_draw_per_column)"
## [1] 1725 3200
## [1] "(nb_donnes I * nb_iter_mcmc J)"

## [1] "mean(table_region$rh98)"
## [1] 8.17064
## [1] "sd(table_region$rh98)"
## [1] 4.228092

## [1] "mean(simulations[,j]) ( truth = 8.171 )"
## [1] 8.018
## [1] "sd(simulations[,j]) ( truth = 4.228 )"
## [1] 4.136

## [1] "mean(simulations[,j]) ( truth = 8.171 )"
## [1] 8.242
## [1] "sd(simulations[,j]) ( truth = 4.228 )"
## [1] 4.081

## [1] "mean(simulations[,j]) ( truth = 8.171 )"
## [1] 8.107
## [1] "sd(simulations[,j]) ( truth = 4.228 )"
## [1] 4.296

## [1] "mean(simulations[,j]) ( truth = 8.171 )"
## [1] 8.124
## [1] "sd(simulations[,j]) ( truth = 4.228 )"
## [1] 4.023

## [1] "mean(simulations[,j]) ( truth = 8.171 )"
## [1] 8.254
## [1] "sd(simulations[,j]) ( truth = 4.228 )"
## [1] 4.377

## [1] "Northern_Congolian_Forest-Savanna_regression_rh98.RDS"
## [1] "########################################"
## [1] "dim(linear_predictors_for_one_beta_draw_per_column)"
## [1]  243 3200
## [1] "(nb_donnes I * nb_iter_mcmc J)"

## [1] "mean(table_region$rh98)"
## [1] 8.251706
## [1] "sd(table_region$rh98)"
## [1] 3.52155

## [1] "mean(simulations[,j]) ( truth = 8.252 )"
## [1] 7.967
## [1] "sd(simulations[,j]) ( truth = 3.522 )"
## [1] 3.848

## [1] "mean(simulations[,j]) ( truth = 8.252 )"
## [1] 8.133
## [1] "sd(simulations[,j]) ( truth = 3.522 )"
## [1] 3.79

## [1] "mean(simulations[,j]) ( truth = 8.252 )"
## [1] 7.529
## [1] "sd(simulations[,j]) ( truth = 3.522 )"
## [1] 3.301

## [1] "mean(simulations[,j]) ( truth = 8.252 )"
## [1] 8.149
## [1] "sd(simulations[,j]) ( truth = 3.522 )"
## [1] 3.831

## [1] "mean(simulations[,j]) ( truth = 8.252 )"
## [1] 8.477
## [1] "sd(simulations[,j]) ( truth = 3.522 )"
## [1] 3.885

## [1] "Sahelian_Acacia_savanna_regression_rh98.RDS"
## [1] "########################################"
## [1] "dim(linear_predictors_for_one_beta_draw_per_column)"
## [1] 5563 3200
## [1] "(nb_donnes I * nb_iter_mcmc J)"

## [1] "mean(table_region$rh98)"
## [1] 3.049537
## [1] "sd(table_region$rh98)"
## [1] 1.187586

## [1] "mean(simulations[,j]) ( truth = 3.05 )"
## [1] 3.036
## [1] "sd(simulations[,j]) ( truth = 1.188 )"
## [1] 0.974

## [1] "mean(simulations[,j]) ( truth = 3.05 )"
## [1] 3.032
## [1] "sd(simulations[,j]) ( truth = 1.188 )"
## [1] 0.987

## [1] "mean(simulations[,j]) ( truth = 3.05 )"
## [1] 3.033
## [1] "sd(simulations[,j]) ( truth = 1.188 )"
## [1] 0.993

## [1] "mean(simulations[,j]) ( truth = 3.05 )"
## [1] 3.036
## [1] "sd(simulations[,j]) ( truth = 1.188 )"
## [1] 0.978

## [1] "mean(simulations[,j]) ( truth = 3.05 )"
## [1] 3.06
## [1] "sd(simulations[,j]) ( truth = 1.188 )"
## [1] 0.989

## [1] "Southern_Congolian_forest-savanna_regression_rh98.RDS"
## [1] "########################################"
## [1] "dim(linear_predictors_for_one_beta_draw_per_column)"
## [1]   47 3200
## [1] "(nb_donnes I * nb_iter_mcmc J)"

## [1] "mean(table_region$rh98)"
## [1] 3.938866
## [1] "sd(table_region$rh98)"
## [1] 2.086246

## [1] "mean(simulations[,j]) ( truth = 3.939 )"
## [1] 3.701
## [1] "sd(simulations[,j]) ( truth = 2.086 )"
## [1] 1.437

## [1] "mean(simulations[,j]) ( truth = 3.939 )"
## [1] 4.2
## [1] "sd(simulations[,j]) ( truth = 2.086 )"
## [1] 2.312

## [1] "mean(simulations[,j]) ( truth = 3.939 )"
## [1] 4.456
## [1] "sd(simulations[,j]) ( truth = 2.086 )"
## [1] 2.167

## [1] "mean(simulations[,j]) ( truth = 3.939 )"
## [1] 4.478
## [1] "sd(simulations[,j]) ( truth = 2.086 )"
## [1] 2.204

## [1] "mean(simulations[,j]) ( truth = 3.939 )"
## [1] 3.967
## [1] "sd(simulations[,j]) ( truth = 2.086 )"
## [1] 2.352

## [1] "West_Sudanian_savanna_regression_rh98.RDS"
## [1] "########################################"
## [1] "dim(linear_predictors_for_one_beta_draw_per_column)"
## [1] 3277 3200
## [1] "(nb_donnes I * nb_iter_mcmc J)"

## [1] "mean(table_region$rh98)"
## [1] 5.728088
## [1] "sd(table_region$rh98)"
## [1] 3.15554

## [1] "mean(simulations[,j]) ( truth = 5.728 )"
## [1] 5.754
## [1] "sd(simulations[,j]) ( truth = 3.156 )"
## [1] 3.108

## [1] "mean(simulations[,j]) ( truth = 5.728 )"
## [1] 5.734
## [1] "sd(simulations[,j]) ( truth = 3.156 )"
## [1] 3.079

## [1] "mean(simulations[,j]) ( truth = 5.728 )"
## [1] 5.776
## [1] "sd(simulations[,j]) ( truth = 3.156 )"
## [1] 3.169

## [1] "mean(simulations[,j]) ( truth = 5.728 )"
## [1] 5.797
## [1] "sd(simulations[,j]) ( truth = 3.156 )"
## [1] 3.108

## [1] "mean(simulations[,j]) ( truth = 5.728 )"
## [1] 5.748
## [1] "sd(simulations[,j]) ( truth = 3.156 )"
## [1] 3.142

## [1] "Western_Congolian_forest-savanna_regression_rh98.RDS"
## [1] "########################################"
## [1] "dim(linear_predictors_for_one_beta_draw_per_column)"
## [1]  259 3200
## [1] "(nb_donnes I * nb_iter_mcmc J)"

## [1] "mean(table_region$rh98)"
## [1] 6.137749
## [1] "sd(table_region$rh98)"
## [1] 4.607916

## [1] "mean(simulations[,j]) ( truth = 6.138 )"
## [1] 6.526
## [1] "sd(simulations[,j]) ( truth = 4.608 )"
## [1] 4.168

## [1] "mean(simulations[,j]) ( truth = 6.138 )"
## [1] 6.45
## [1] "sd(simulations[,j]) ( truth = 4.608 )"
## [1] 4.353

## [1] "mean(simulations[,j]) ( truth = 6.138 )"
## [1] 7.079
## [1] "sd(simulations[,j]) ( truth = 4.608 )"
## [1] 5.042

## [1] "mean(simulations[,j]) ( truth = 6.138 )"
## [1] 5.607
## [1] "sd(simulations[,j]) ( truth = 4.608 )"
## [1] 3.163

## [1] "mean(simulations[,j]) ( truth = 6.138 )"
## [1] 6.369
## [1] "sd(simulations[,j]) ( truth = 4.608 )"
## [1] 3.703